The introduction of flexible frequency grids and advanced modulation techniques to optical transmission, namely an elastic optical network, requires new routing and spectrum allocation techniques. In this paper, we investigate dynamic two-step routing and spectrum allocation (RSA) methods for elastic optical networks. K-shortest path-based methods as well as spectrum allocation methods are analysed and discussed. Experimental verification of the investigated techniques is provided using simulation software. Simulation results present effectiveness of routing and spectrum allocation methods for analyzed networks using requested bandwidth of connections. Moreover, performance of shortest path first methods improves considerably when a number of candidate paths increases in the UBN24 topology.